Applied Functional Analysis

J. Tinsley Oden is the Director of the Institute for Computational Engineering and Sciences (ICES) and Associate Vice President forResearch at The University of Texas at Austin. Dr. Oden is also a member of the US National Academy of Engineering and therecipient of the 2009 SIAM Distinguished Career Award. He holds five honorary doctorates and was knighted Chevalier de l’Ordredes Palmes Académiques by the French government.Leszek F. Demkowicz is the Assistant Director of ICES and a professor in the Department of Aerospace Engineering andEngineering Mechanics at The University of Texas at Austin. Dr. Demkowicz was one of the founding members of the PolishAssociation for Computational Mechanics (PACM), serving as its first president from 1991 to 1993. His recent research has beensummarized in the two volumes Computing with hp-ADAPTIVE FINITE ELEMENTS (CRC Press, 2007 and 2008). For his work onhp methods, he was awarded the 2009 Zienkiewicz Medal by PACM and the 2009 Computational and Applied Sciences Award bythe United States Association for Computational Mechanics (USACM).

• Preliminaries Elementary Logic and Set Theory Relations; Functions Cardinality of Sets Foundations of Abstract Algebra Elementary Topology in Rn Elements of Differential and Integral CalculusLinear Algebra Vector Spaces—The Basic Concepts Linear Transformations Algebraic Duals; Euclidean SpacesLebesgue Measure and IntegrationLebesgue MeasureLebesgue Integration TheoryTopological and Metric SpacesElementary TopologyTheory of Metric Spaces Banach SpacesTopological Vector SpacesHahn–Banach Extension TheoremBounded (Continuous) Linear Operators on Normed SpacesClosed OperatorsTopological DualsWeak CompactnessClosed Range TheoremSolvability of Linear EquationsHilbert SpacesBasic TheoryDuality in Hilbert SpacesElements of Spectral TheoryReferences